Olympic Tracing Challenge
Can you trace this
entire
figure?
Things to keep in mind while tracing:
No picking up your writing or tracing tool.
No doubling back along a line already traced.
Bonus :
- If it's impossible, can you prove why?
- If it's possible, how many different ways there to accomplish the tracing if you must start at one of the intersection points?
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This is one of my favorite tracing puzzles because most people fail the first time they try to trace (I've even seen some mathematicians fail when they first try to trace it out, even though they are certain that it's possible theoretically! :D).
So, yes, it's a trap. ;-) It's easy to get stuck thinking about the figure as a collection of overlapping circles, the 5 Olympic rings in particular. They're usually colored like this:
When you think about the rings this way, it's easy to get stuck when tracing, tempted by a natural desire to finish an entire ring before moving on to the next part of the design. However, given a different perspective on the same figure, as colored below, here is a simple tracing strategy:
(1) Start anywhere on the black curve.
(2) Trace along the black curve until you hit a colored leaf, as soon as you do, take a break from black and trace that entire colored leaf (both sides). In doing so, you'll return to where you paused on the black curve and can continue to on to the next leaf and so on. Continue until you return to where you started on the black curve.
If you think about this figure colored as it's colored above, it becomes far easier to trace the figure & also to further study the puzzle in more depth mathematically. For example, after you've found your own path for tracing this figure, can you figure out how many different ways there actually are to accomplish the tracing if you must start at one of the 8 intersection points?